Percolation and spin-glass behavior in stage-2 ${\mathrm{Co}}_c{\mathrm{Mg}}_{1-c}{\mathrm{Cl}}_2$ graphite intercalation compounds

Stage-2 ${\mathrm{Co}}_c{\mathrm{Mg}}_{1-c}{\mathrm{Cl}}_2$ graphite intercalation compounds magnetically behave like quasi-two-dimensional (2D) XY-like site-diluted ferromagnets on the triangular lattice. The percolation and spin-glass behavior of these compounds has been studied using superconducting quantum interference device (SQUID) ac magnetic susceptibility $({\chi }_{\mathrm{aa}}^{\prime }$ and ${\chi }_{\mathrm{aa}}^{″})$ and SQUID dc magnetization. The pure system $\mathrm{}(c=1\mathrm{})\mathrm{}$ undergoes two magnetic phase transitions at $T_{\mathrm{cu}}$ and $T_{\mathrm{cl}}.$ 2D ferromagnetic long range order exists between $T_{\mathrm{cu}}$ and $T_{\mathrm{cl}}.$ The critical temperature $T_{\mathrm{cl}}$ decreases to zero at the percolation threshold $c_p=0.5,$ while $T_{\mathrm{cu}}$ above $c_p$ decreases with decreasing Co concentration and may be connected to a crossover temperature $T_x$ below $c_p.$ A spin-glass-like behavior is observed for $c=0.3\mathrm{}$ and 0.46. Spin frustration occurs because of the competition between the ferromagnetic intraplanar exchange interaction and an effective antiferromagnetic interplanar exchange interaction which is not large enough to give rise to three-dimensional antiferromagnetic correlation.